Problem: $A$ $B$ $C$ If: $ AB = 8x + 5$, $ AC = 85$, and $ BC = 5x + 2$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {8x + 5} + {5x + 2} = {85}$ Combine like terms: $ 13x + 7 = {85}$ Subtract $7$ from both sides: $ 13x = 78$ Divide both sides by $13$ to find $x$ $ x = 6$ Substitute $6$ for $x$ in the expression that was given for $BC$ $ BC = 5({6}) + 2$ Simplify: $ {BC = 30 + 2}$ Simplify to find ${BC}$ : $ {BC = 32}$